# Bernoulli equation in open vs. closed systems

Can we apply Bernoulli equation to a closed system the same way we apply it to an open system? In an open system increasing the speed of the fluid implies that either the pressure or GPE should decrease as a result of conserving energy. I wounder how would this apply to a closed system?

In a closed system where there is no flow and thus velocity = 0, Bernoulli's equation is reduced to $$P_1 + \rho gz_1 = P_2 + \rho g z_2$$ $$P_2= P1 - \rho g \Delta z$$ which is really just the normal rule for pressure in liquids. In gases usually $$\rho$$ is too small so the pressure is constant throughout the gas. So basically it is reduced to the normal rules you use for fluid statics.